78.9.4 problem 4 (a)

Internal problem ID [18252]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 4 (a)
Date solved : Tuesday, January 28, 2025 at 11:44:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(x^3*diff(y(x),x$2)+ x^2*diff(y(x),x) +x*y(x)=1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 25

DSolve[x^3*D[y[x],{x,2}] +x^2*D[y[x],x] +x*y[x] ==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2 x}+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \]