77.1.33 problem 50 (page 56)

Internal problem ID [17923]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 50 (page 56)
Date solved : Tuesday, January 28, 2025 at 11:12:47 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=k y+f \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x)=k*y(x)+f(x),y(x), singsol=all)
 

\[ y = \left (\int f \,{\mathrm e}^{-k x}d x +c_{1} \right ) {\mathrm e}^{k x} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 32

DSolve[D[y[x],x]==k*y[x]+f[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{k x} \left (\int _1^xe^{-k K[1]} f(K[1])dK[1]+c_1\right ) \]