Internal problem ID [14775]
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: 65.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 10, y^{\prime \prime }\left (1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve([x^3*diff(y(x),x$3)+9*x^2*diff(y(x),x$2)+44*x*diff(y(x),x)+58*y(x)=0,y(1) = 2, D(y)(1) = 10, (D@@2)(y)(1) = -2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {106}{25}+\frac {14 \sin \left (5 \ln \left (x \right )\right )}{5}-\frac {56 \cos \left (5 \ln \left (x \right )\right )}{25}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[{x^3*y'''[x]+9*x^2*y''[x]+44*x*y'[x]+58*y[x]==0,{y[1]==2,y'[1]==10,y''[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {70 \sin (5 \log (x))-56 \cos (5 \log (x))+106}{25 x^2} \]