29.1.1 problem 0

Internal problem ID [4608]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 0
Date solved : Monday, January 27, 2025 at 09:26:09 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y \left (x \right ) = a \left (\int f \left (x \right )d x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 20

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

\[ y(x)\to \int _1^xa f(K[1])dK[1]+c_1 \]