60.1.103 problem 103

Internal problem ID [10117]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 103
Date solved : Monday, January 27, 2025 at 06:28:07 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(x*diff(y(x),x) + x*y(x)^2 - (2*x^2+1)*y(x) - x^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 38

DSolve[x*D[y[x],x] + x*y[x]^2 - (2*x^2+1)*y[x] - x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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