Internal problem ID [14748]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y=\frac {1}{x^{2}}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([2*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-y(x)=1/x^2,y(1) = 0, D(y)(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {22 x^{\frac {5}{2}}-25 x +3}{15 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 24
DSolve[{2*x^2*y''[x]+3*x*y'[x]-y[x]==1/x^2,{y[1]==0,y'[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {22 x^{5/2}-25 x+3}{15 x^2} \]