Internal problem ID [7741]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 161.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((x^2-5*x+6)*diff(y(x),x) + 3*x*y(x) - 8*y(x) + x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-\frac {1}{4} x^{4}+\frac {2}{3} x^{3}+c_{1}}{\left (x -2\right )^{2} \left (x -3\right )} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 33
DSolve[(x^2-5*x+6)*y'[x] + 3*x*y[x] - 8*y[x] + x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(8-3 x) x^3-12 c_1}{12 (x-3) (x-2)^2} \\ \end{align*}