Internal problem ID [13507]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.6 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }+4 y^{\prime }=18 x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 8, y^{\prime }\left (1\right ) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([x*diff(y(x),x$2)+4*diff(y(x),x)=18*x^2,y(1) = 8, D(y)(1) = -3],y(x), singsol=all)
\[ y \left (x \right ) = x^{3}+\frac {2}{x^{3}}+5 \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 15
DSolve[{x*y''[x]+4*y'[x]==18*x^2,{y[1]==8,y'[1]==-3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3+\frac {2}{x^3}+5 \]