29.9.22 problem 262

Internal problem ID [4862]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 262
Date solved : Monday, January 27, 2025 at 09:43:39 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 53

dsolve(x^2*diff(y(x),x)+a*x^2+b*x*y(x)+c*y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x \left (\sqrt {4 a c -b^{2}-2 b -1}\, \tan \left (\frac {\sqrt {4 a c -b^{2}-2 b -1}\, \left (\ln \left (x \right )+c_{1} \right )}{2}\right )+b +1\right )}{2 c} \]

✓ Solution by Mathematica

Time used: 60.163 (sec). Leaf size: 66

DSolve[x^2 D[y[x],x]+a x^2 +b x y[x]+c y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x \left (-\sqrt {4 a c-b^2-2 b-1} \tan \left (\frac {1}{2} \sqrt {4 a c-b^2-2 b-1} (-\log (x)+c_1)\right )+b+1\right )}{2 c} \]