82.39.4 problem Ex. 4

Internal problem ID [18936]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:37:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve((x+a)^2*diff(y(x),x$2)-4*(x+a)*diff(y(x),x)+6*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 33

DSolve[(x+a)^2*D[y[x],{x,2}]-4*(x+a)*D[y[x],x]+6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} (2 a+3 x)+c_2 (a+x)^3+c_1 (a+x)^2 \]