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

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\[y^\prime+u\left(x\right)y=f\left(x\right), y\left(x_0\right)=k \] (1) this is a linear ODE. Let’s substitute \[A\left(x\right)=e^{\int_{x_0}^{x}u\left(t\right)dt}\]into eqn (1)and differentiating it…

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