60.1.162 problem 163

Internal problem ID [10176]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 163
Date solved : Monday, January 27, 2025 at 06:31:22 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.444 (sec). Leaf size: 43

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

\[ y(x)\to -\sqrt {-a^2} \sqrt {x} \tan \left (\frac {2 \sqrt {-a^2}}{\sqrt {x}}-c_1\right ) \]