60.1.182 problem 183

Internal problem ID [10196]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 183
Date solved : Monday, January 27, 2025 at 06:37:33 PM
CAS classification : [_separable]

\begin{align*} \left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve((2*x^4-x)*diff(y(x),x) - 2*(x^3-1)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{2}}{\left (2 x^{3}-1\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 42

DSolve[(2*x^4-x)*D[y[x],x] - 2*(x^3-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\frac {2-2 K[1]^3}{K[1]-2 K[1]^4}dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}