74.15.46 problem 49

Internal problem ID [16485]
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 : 49
Date solved : Tuesday, January 28, 2025 at 09:09:18 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)+37*x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\sin \left (6 \ln \left (x \right )\right ) c_{2} +c_{3} \cos \left (6 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 60.082 (sec). Leaf size: 39

DSolve[x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]+37*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {c_2 \cos (6 \log (K[1]))+c_1 \sin (6 \log (K[1]))}{K[1]}dK[1]+c_3 \]