60.1.142 problem 143

Internal problem ID [10156]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 143
Date solved : Monday, January 27, 2025 at 06:30:20 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Riccati, _special]]

\begin{align*} x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 40

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

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

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 77

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

\begin{align*} y(x)\to -\frac {-1+\sqrt {4 a b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {4 a b+1}}+c_1}\right )}{2 a x} \\ y(x)\to -\frac {\sqrt {4 a b+1}-1}{2 a x} \\ \end{align*}