53.4.8 problem 9

Internal problem ID [8496]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:07:24 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }&=y^{\prime }+x^{5} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}}\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 16

dsolve([x*diff(y(x),x$2)=diff(y(x),x)+x^5,y(1) = 1/2, D(y)(1) = 1],y(x), singsol=all)
 

\[ y = \frac {1}{24} x^{6}+\frac {3}{8} x^{2}+\frac {1}{12} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

DSolve[{x*D[y[x],{x,2}]==D[y[x],x]+x^5,{y[1]==1/2,Derivative[1][y][1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} \left (x^6+9 x^2+2\right ) \]