Internal problem ID [13833]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -9 y=3 \sqrt {x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {35 c_{1} x^{6}-12 x^{\frac {7}{2}}+35 c_{2}}{35 x^{3}} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 27
DSolve[x^2*y''[x]+x*y'[x]-9*y[x]==3*Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^3+\frac {c_1}{x^3}-\frac {12 \sqrt {x}}{35} \]