Ordinary Differential Equations (ODE) Calculator - Symbolab

Free ordinary differential equations (ODE) calculator - solve ordinary differential equations (ODE) step-by-step. UpgradetoPro Continuetosite Thiswebsiteusescookiestoensureyougetthebestexperience. Byusingthiswebsite,youagreetoourCookiePolicy.Learnmore Accept Solutions Graphing Practice New Geometry Calculators Notebook   Groups CheatSheets SignIn Upgrade Upgrade AccountDetails LoginOptions AccountManagement Settings Subscription Logout   Nonewnotifications en English Español Português Français 中文(简体) TiếngViệt עברית العربية PreAlgebra OrderofOperations Factors&Primes Fractions LongArithmetic Decimals Exponents&Radicals Ratios&Proportions Percent Modulo Mean,Median&Mode ScientificNotationArithmetics Algebra Equations Inequalities SystemofEquations SystemofInequalities BasicOperations AlgebraicProperties PartialFractions Polynomials RationalExpressions Sequences PowerSums Pi(Product)Notation Induction LogicalSets WordProblems PreCalculus Equations Inequalities SimultaneousEquations SystemofInequalities Polynomials Rationales ComplexNumbers Polar/Cartesian Functions Arithmetic&Comp. CoordinateGeometry PlaneGeometry SolidGeometry ConicSections Trigonometry Calculus Derivatives DerivativeApplications Limits Integrals IntegralApplications IntegralApproximation Series ODE MultivariableCalculus LaplaceTransform Taylor/MaclaurinSeries FourierSeries Functions LineEquations Functions Arithmetic&Comp. ConicSections Transformation Matrices&Vectors Matrices Vectors Trigonometry Identities ProvingIdentities TrigEquations TrigInequalities EvaluateFunctions Simplify Statistics ArithmeticMean GeometricMean QuadraticMean Median Mode Order Minimum Maximum Probability Mid-Range Range StandardDeviation Variance LowerQuartile UpperQuartile InterquartileRange Midhinge StandardNormalDistribution Physics Mechanics Chemistry ChemicalReactions ChemicalProperties Finance SimpleInterest CompoundInterest PresentValue FutureValue Economics PointofDiminishingReturn Conversions DecimaltoFraction FractiontoDecimal RadianstoDegrees DegreestoRadians Hexadecimal ScientificNotation Distance Weight Time OrdinaryDifferentialEquations(ODE)Calculator Solveordinarydifferentialequations(ODE)step-by-step DerivativesFirstDerivativeWRTNewSpecifyMethodChainRuleProductRuleQuotientRuleSum/DiffRule SecondDerivativeThirdDerivativeHigherOrderDerivativesDerivativeatapointPartialDerivativeImplicitDerivativeSecondImplicitDerivativeDerivativeusingDefinition DerivativeApplicationsTangentNormalCurvedLineSlopeExtremePointsTangenttoConicLinearApproximationNew LimitsOneVariableMultiVariableLimitOneSidedAtInfinitySpecifyMethodNewL'Hopital'sRuleSqueezeTheoremChainRuleFactoringSubstitutionSandwichTheorem IntegralsIndefiniteIntegralsDefiniteIntegralsSpecific-MethodPartialFractionsU-SubstitutionTrigonometricSubstitutionByPartsLongDivision ImproperIntegralsAntiderivativesDoubleIntegralsTripleIntegralsMultipleIntegrals IntegralApplicationsLimitofSumAreaundercurveAreabetweencurvesAreaunderpolarcurveVolumeofsolidofrevolutionArcLengthFunctionAverage IntegralApproximationNewRiemannSumTrapezoidalSimpson'sRuleMidpointRule SeriesConvergenceGeometricSeriesTestTelescopingSeriesTestAlternatingSeriesTestPSeriesTestDivergenceTestRatioTestRootTestComparisonTestLimitComparisonTestIntegralTest AbsoluteConvergencePowerSeriesRadiusofConvergenceNewIntervalofConvergenceNew ODELinearFirstOrderLinearw/constantcoefficientsNewSeparableBernoulliExactSecondOrderHomogenousNonHomogenousSubstitutionSystemofODEsIVPusingLaplaceNewSeriesSolutionsNewMethodofFrobeniusNew MultivariableCalculusNewPartialDerivativeImplicitDerivativeTangenttoConicMultiVariableLimitMultipleIntegralsGradientNewDivergenceNewExtremePointsNew LaplaceTransformTransformInverse Taylor/MaclaurinSeriesTaylorSeriesMaclaurinSeries FourierSeries fullpad» x^2 x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partialx} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) H_{2}O ▭\:\longdivision{▭} \times\twostack{▭}{▭} +\twostack{▭}{▭} -\twostack{▭}{▭} \left( \right) \times \square\frac{\square}{\square} \bold{\mathrm{Basic}} \bold{\alpha\beta\gamma} \bold{\mathrm{AB\Gamma}} \bold{\sin\cos} \bold{\ge\div\rightarrow} \bold{\overline{x}\space\mathbb{C}\forall} \bold{\sum\space\int\space\product} \bold{\begin{pmatrix}\square&\square\\\square&\square\end{pmatrix}} \bold{H_{2}O} \square^{2} x^{\square} \sqrt{\square} \nthroot[\msquare]{\square} \frac{\msquare}{\msquare} \log_{\msquare} \pi \theta \infty \int \frac{d}{dx} \ge \le \cdot \div x^{\circ} (\square) |\square| (f\:\circ\:g) f(x) \ln e^{\square} \left(\square\right)^{'} \frac{\partial}{\partialx} \int_{\msquare}^{\msquare} \lim \sum \sin \cos \tan \cot \csc \sec \alpha \beta \gamma \delta \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega A B \Gamma \Delta E Z H \Theta K \Lambda M N \Xi \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \sin \cos \tan \cot \sec \csc \sinh \cosh \tanh \coth \sech \arcsin \arccos \arctan \arccot \arcsec \arccsc \arcsinh \arccosh \arctanh \arccoth \arcsech \begin{cases}\square\\\square\end{cases} \begin{cases}\square\\\square\\\square\end{cases} = \ne \div \cdot \times < > \le \ge (\square) [\square] ▭\:\longdivision{▭} \times\twostack{▭}{▭} +\twostack{▭}{▭} -\twostack{▭}{▭} \square! x^{\circ} \rightarrow \lfloor\square\rfloor \lceil\square\rceil \overline{\square} \vec{\square} \in \forall \notin \exist \mathbb{R} \mathbb{C} \mathbb{N} \mathbb{Z} \emptyset \vee \wedge \neg \oplus \cap \cup \square^{c} \subset \subsete \superset \supersete \int \int\int \int\int\int \int_{\square}^{\square} \int_{\square}^{\square}\int_{\square}^{\square} \int_{\square}^{\square}\int_{\square}^{\square}\int_{\square}^{\square} \sum \prod \lim \lim_{x\to\infty} \lim_{x\to0+} \lim_{x\to0-} \frac{d}{dx} \frac{d^2}{dx^2} \left(\square\right)^{'} \left(\square\right)^{''} \frac{\partial}{\partialx} (2\times2) (2\times3) (3\times3) (3\times2) (4\times2) (4\times3) (4\times4) (3\times4) (2\times4) (5\times5) (1\times2) (1\times3) (1\times4) (1\times5) (1\times6) (2\times1) (3\times1) (4\times1) (5\times1) (6\times1) (7\times1) \mathrm{Radians} \mathrm{Degrees} \square! ( ) % \mathrm{clear} \arcsin \sin \sqrt{\square} 7 8 9 \div \arccos \cos \ln 4 5 6 \times \arctan \tan \log 1 2 3 - \pi e x^{\square} 0 . \bold{=} + MostUsedActions \mathrm{laplace} \mathrm{bernoulli} \mathrm{substitution} \mathrm{linear} \mathrm{exact} SeeAll area asymptotes criticalpoints derivative domain eigenvalues eigenvectors expand extremepoints factor implicitderivative inflectionpoints intercepts inverse laplace inverselaplace partialfractions range slope simplify solvefor tangent taylor vertex geometrictest alternatingtest telescopingtest pseriestest roottest Go Related» Graph» NumberLine» Similar» Examples» Ouronlineexperttutorscananswerthisproblem Getstep-by-stepsolutionsfromexperttutorsasfastas15-30minutes. Yourfirst5questionsareonus! Startyourfreetrial Inpartnershipwith YouarebeingredirectedtoCourseHero IwanttosubmitthesameproblemtoCourseHero Cancel Proceed CorrectAnswer:) Let'sTryAgain:( Trytofurthersimplify Verify   Related NumberLine Graph HidePlot» Sorry,yourbrowserdoesnotsupportthisapplication Viewinteractivegraph> Examples 2y'-y=4\sin(3t) ty'+2y=t^2-t+1 y'=e^{-y}(2x-4) \frac{dr}{d\theta}=\frac{r^2}{\theta} y'+\frac{4}{x}y=x^3y^2 y'+\frac{4}{x}y=x^3y^2,y(2)=-1 laplace\:y^{\prime}+2y=12\sin(2t),y(0)=5 bernoulli\:\frac{dr}{dθ}=\frac{r^2}{θ} ordinary-differential-equation-calculator en image/svg+xml RelatedSymbolabblogposts AdvancedMathSolutions–OrdinaryDifferentialEquationsCalculator Differentialequationscontainderivatives,solvingtheequationinvolvesintegration(toget... ReadMore ©CourseHeroSymbolab2021 Home What'sNew Blog About Privacy Terms PopularProblems Help Wewantyourfeedback (optional) (optional) Pleaseaddamessage. Messagereceived.Thanksforthefeedback. Cancel Send GeneratingPDF... Feedback