Internal problem ID [13552]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.3 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -y=\sqrt {x}} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=sqrt(x),x],singsol=all)
\[ y \left (x \right ) = \frac {3 c_{2} x^{2}-4 x^{\frac {3}{2}}+3 c_{1}}{3 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 25
DSolve[x^2*y''[x]+x*y'[x]-y[x]==Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {4 \sqrt {x}}{3}+\frac {c_1}{x}+c_2 x \]