Internal problem ID [5427]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x y^{\prime \prime }+2 y^{\prime }+4 y x=4} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)+4*x*y(x)=4,y(x), singsol=all)
\[ y = \frac {c_{2} \sin \left (2 x \right )}{x}+\frac {c_{1} \cos \left (2 x \right )}{x}+\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 38
DSolve[x*y''[x]+2*y'[x]+4*x*y[x]==4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 c_1 e^{-2 i x}-i c_2 e^{2 i x}+4}{4 x} \]