73.17.35 problem 35

Internal problem ID [15569]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:02:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=3 \sqrt {x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 24

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=3*sqrt(x),y(x), singsol=all)
 

\[ y = \frac {35 c_{1} x^{6}-12 x^{{7}/{2}}+35 c_{2}}{35 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-9*y[x]==3*Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^3+\frac {c_1}{x^3}-\frac {12 \sqrt {x}}{35} \]