73.14.21 problem 21.15 (c)

Internal problem ID [15431]
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)
Date solved : Tuesday, January 28, 2025 at 07:55:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=4 x^{2}+2 x +3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = c_{2} x^{5}+c_{1} x^{3}+\frac {1}{5}+\frac {4}{3} x^{2}+\frac {1}{4} x \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 33

DSolve[x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+15*y[x]==4*x^2+2*x+3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^5+c_1 x^3+\frac {4 x^2}{3}+\frac {x}{4}+\frac {1}{5} \]