40.13.16 problem 37

Internal problem ID [6770]
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 : 37
Date solved : Monday, January 27, 2025 at 02:30:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=4 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

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

\[ y = \frac {1+\sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 38

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

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