29.5.18 problem 134

Internal problem ID [4735]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 134
Date solved : Monday, January 27, 2025 at 09:34:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

\[ x -\frac {\int _{}^{y \left (x \right )}\frac {1}{f \left (\textit {\_a} \right )}d \textit {\_a}}{a}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 35

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\&\right ][a x+c_1] \\ y(x)\to f^{(-1)}(0) \\ \end{align*}