29.9.10 problem 250

Internal problem ID [4850]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 250
Date solved : Monday, January 27, 2025 at 09:42:42 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

\[ y \left (x \right ) = -b -\frac {a}{2 x}+x c \ln \left (x \right )+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 32

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

\[ y(x)\to -\frac {a}{2 x}-b-\frac {3 c x}{2}+c x \log (x)+c_1 x \]