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solve dy/dt=yt^3-1.5y subject to y(0)=1

By SK Math Expert June 2, 2021ODEs, UncategorizedFirst order odes

Introduction : Here we shall solve dy/dt=yt^3-1.5y subject to y(0)=1 which is a ordinary differential equation of first order with a condition on solution. Question : Solve \[\frac{dy}{dt}=yt^3-1.5y , y(0)=1\]…

Bernoulli Differential Equation definition and examples

By SK Math Expert May 26, 2021ODEsODEs

Introduction : Here we shall introduce definition of Bernoulli Differential Equation and solved examples. Bernoulli Differential Equation A differential equation is called Bernoulli Differential Equation if it can be written…

Solved Van Der Val ODE solution long term behaviour

By SK Math Expert May 13, 2021ODEsNon Linear ODEs

Introduction : Van Der Val ODE is a second order differential equation. To analyse it's solution behaviour First we convert it into a system of first order ODEs then obtained…

solved particular integral of linear ode dy/dt+cos(t)y=3cos(t)

By SK Math Expert May 13, 2021ODEsLinear ODEs

Introduction : The differential equation dy/dt+cos(t)y=3cos(t) is a linear ode. We shall apply integrating factor method to solve this. Finally using initial condition we shall get it's particular integral. Question…

Solve system of initial value problems example 2

By SK Math Expert April 25, 2021ODEssystem of differential equations

Introduction: In this question, we explain how to solve system of initial value problems example is given in the following solution. Question: Solve system of initial value problems \[u^\prime=-0.2\left(v-2\right), u\left(0\right)=2…

power series solution about x0 =0 example 1

By SK Math Expert April 24, 2021ODEspower series solution of ODEs

Introduction: In this question, we find power series solution about x0 =0 example 1 of an Ordinary differential equation. Step by step solution is given below Question: Find power series…

How to solve ODE y'(x)+u(x)y(x)=f(x)

By SK Math Expert April 11, 2021ODEsFirst order odes

Introduction: In this solution, an step by step procedure of How to solve ODE y'(x)+u(x)y(x)=f(x) is explained. Question : Solve \[y^\prime+u\left(x\right)y=f\left(x\right), y\left(x_0\right)=k \] Solution: We have given ode \[y^\prime+u\left(x\right)y=f\left(x\right), y\left(x_0\right)=k…