29.11.27 problem 318

Internal problem ID [4918]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 318
Date solved : Monday, January 27, 2025 at 09:50:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 27

dsolve((x-2)*(x-3)*diff(y(x),x)+x^2-8*y(x)+3*x*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 34

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

\[ y(x)\to \frac {-3 x^4+8 x^3-12 c_1}{12 (x-3) (x-2)^2} \]