60.1.97 problem 97

Internal problem ID [10111]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 97
Date solved : Monday, January 27, 2025 at 06:27:52 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 32

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a K[1]^2+b}dK[1]=-x+c_1,y(x)\right ] \]