First order odes

Introduction : Here we shall solve dy/dt=y-2t^2y subject to initial condition y(0)=2 which is a ordinary differential equation of first order with a condition on solution. Question : Solve \[dy/dt=y-2t^2y,…

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\ \…

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…