7.5.48 problem 48

Internal problem ID [152]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 48
Date solved : Friday, February 07, 2025 at 07:58:48 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y = -\frac {c_1}{2 x^{2}}+\ln \left (x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {c_1}{2 x^2}+\log (x)+c_2 \]