20.1.31 problem Problem 39

Internal problem ID [3588]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 39
Date solved : Monday, January 27, 2025 at 07:46:47 AM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=6 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 19

dsolve([diff(y(x),x$3)=6*x,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -4],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{4} x^{4}-2 x^{2}+1-x \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

DSolve[{D[y[x],{x,3}]==6*x,{y[0]==2,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (x^4-8 x^2-4 x+8\right ) \]