7.5.46 problem 46

Internal problem ID [150]
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 : 46
Date solved : Friday, February 07, 2025 at 07:58:45 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+y^{\prime }&=4 x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(x*diff(y(x),x$2)+diff(y(x),x)=4*x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 16

DSolve[x*D[y[x],{x,2}]+D[y[x],x]==4*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+c_1 \log (x)+c_2 \]