60.1.172 problem 173

Internal problem ID [10186]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 173
Date solved : Monday, January 27, 2025 at 06:34:19 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(x^3*diff(y(x),x) - x^6*y(x)^2 - (2*x-3)*x^2*y(x) + 3=0,y(x), singsol=all)
 

\[ y = \frac {-3 \,{\mathrm e}^{4 x} c_{1} -3}{x^{3} \left ({\mathrm e}^{4 x} c_{1} -3\right )} \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 34

DSolve[x^3*D[y[x],x] - x^6*y[x]^2 - (2*x-3)*x^2*y[x] + 3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3} \\ y(x)\to -\frac {3}{x^3} \\ \end{align*}