Internal problem ID [13695]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.15 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y=4 x^{2}+2 x +3} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+15*y(x)=4*x^2+2*x+3,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{5}+\frac {4}{3} x^{2}+\frac {1}{4} x \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 33
DSolve[x^2*y''[x]-7*x*y'[x]+15*y[x]==4*x^2+2*x+3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^5+c_1 x^3+\frac {4 x^2}{3}+\frac {x}{4}+\frac {1}{5} \]