29.9.13 problem 253

Internal problem ID [4853]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 253
Date solved : Monday, January 27, 2025 at 09:42:46 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 22

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

\[ y(x)\to -\frac {a}{b x+x}+c_1 x^b \]