29.12.19 problem 338

Internal problem ID [4938]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 338
Date solved : Monday, January 27, 2025 at 09:52:49 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.257 (sec). Leaf size: 23

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

\[ y(x)\to \frac {x \tan \left (\frac {b (\log (x)+a c_1)}{a}\right )}{b} \]