29.5.20 problem 136

Internal problem ID [4737]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 136
Date solved : Monday, January 27, 2025 at 09:34:54 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.255 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{g(K[1])}dK[1]\&\right ]\left [\int _1^xf(K[2])dK[2]+c_1\right ] \\ y(x)\to g^{(-1)}(0) \\ \end{align*}