60.1.160 problem 161

Internal problem ID [10174]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 161
Date solved : Monday, January 27, 2025 at 06:31:17 PM
CAS classification : [_linear]

\begin{align*} \left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \frac {-\frac {1}{4} x^{4}+\frac {2}{3} x^{3}+c_{1}}{\left (x -3\right ) \left (x -2\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 93

DSolve[(x^2-5*x+6)*D[y[x],x] + 3*x*y[x] - 8*y[x] + x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {8-3 K[1]}{K[1]^2-5 K[1]+6}dK[1]\right ) \left (\int _1^x-\frac {\exp \left (-\int _1^{K[2]}\frac {8-3 K[1]}{K[1]^2-5 K[1]+6}dK[1]\right ) K[2]^2}{K[2]^2-5 K[2]+6}dK[2]+c_1\right ) \]