29.3.13 problem 67

Internal problem ID [4675]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 67
Date solved : Monday, January 27, 2025 at 09:31:06 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=a x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x) = a*x*y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {2}{a \,x^{2}-2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 24

DSolve[D[y[x],x]==a x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2}{a x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}