solve dy/dt=ty-t^2y such that y(0)=e
Introduction : Here we shall solve dy/dt=ty-t^2y such that y(0)=e which is a ordinary differential equation of first order with a condition on solution. Question : Solve \[\frac{dy}{dt}=ty\ -t^2y\ \…
solve dy/dt=yt^3-1.5y subject to y(0)=1
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 \[\frac{dy}{dt}=yt^3-1.5y , y(0)=1\]…
find steady state solution of heat equation
Introduction : Here we shall determine steady state solution of heat equation. Steady state solution is a time independent function that satisfies the given PDE. Question : find steady state…
Prove that the Steady state solution of heat equation is unique
Introduction : Here we shall Prove that the Steady state solution of heat equation is unique. Question : Given heat equation \[u_t=u_{xx}\ \ ,\ 0<x<1,\ t>0 \] \[\ u\left(0,t\right)=0\ ,\…
prove that derivative of cos(x) is -sin(x)
Introduction : In this we shall prove that the derivative of cos(x) is -sin(x) using the formal definition of derivative. Question : prove that derivative of cos(x) is -sin(x) Solution…
solve linear system matlab example 11x-3y=6 5x+2y=9
Introduction : Here we shall write and explain line by line matlab program to solve linear system matlab example following. Question : Solve linear system \[11x-3y=6, 5x+2y=9\] Solution : Given…
Finite difference method to solve Boundary value problem y”+8y=0
Introduction : Int this question, we shall apply Finite difference method to solve Boundary value problem y''+8y=0 subject to conditions T[16]=35, dT/dx(x=0)=125 Question : Apply Finite difference method to solve…
Bernoulli Differential Equation definition and examples
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…
how to solve second order ode by Laplace transform method example 2
Introduction : Here we present the step by step answer of the question how to solve second order ode by Laplace transform method example 2 given below. Question : how…
how to solve differential equation x”+4x=delta(t-2) x(0) =1 x'(0)=-2 by Laplace transform method
Introduction : Here we shall explain step by step answer of how to solve differential equation x''+4x=delta(t-2) x(0) =1 x'(0)=-2 by Laplace transform method. Question : How to solve differential…