40.13.3 problem 23

Internal problem ID [6757]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:27:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=8 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve((x^2+4)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=8,y(x), singsol=all)
 

\[ y = c_1 \,x^{2}+c_2 x -4 c_1 +4 \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 22

DSolve[(x^2+4)*D[y[x],{x,2}]-2*x*D[y[x],x]+2*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 (x-2 i)^2-c_2 x+4 \]