60.1.174 problem 175

Internal problem ID [10188]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 175
Date solved : Monday, January 27, 2025 at 06:34:24 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.275 (sec). Leaf size: 93

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

\[ y(x)\to \exp \left (\int _1^x\frac {1-2 K[1]^2}{K[1]-K[1]^3}dK[1]\right ) \left (\int _1^x\frac {a \exp \left (-\int _1^{K[2]}\frac {1-2 K[1]^2}{K[1]-K[1]^3}dK[1]\right ) K[2]^2}{1-K[2]^2}dK[2]+c_1\right ) \]