60.1.102 problem 102

Internal problem ID [10116]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 102
Date solved : Monday, January 27, 2025 at 06:28:04 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }+x y^{2}-y-a \,x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 36

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

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