74.15.66 problem 65

Internal problem ID [16505]
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
Date solved : Tuesday, January 28, 2025 at 09:09:53 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y&=0 \end{align*}

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: 0.026 (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)
 

\[ y = \frac {\frac {106}{25}+\frac {14 \sin \left (5 \ln \left (x \right )\right )}{5}-\frac {56 \cos \left (5 \ln \left (x \right )\right )}{25}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 28

DSolve[{x^3*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]+44*x*D[y[x],x]+58*y[x]==0,{y[1]==2,Derivative[1][y][1]==10,Derivative[2][y][1]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {70 \sin (5 \log (x))-56 \cos (5 \log (x))+106}{25 x^2} \]