73.14.10 problem 21.12

Internal problem ID [15420]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.12
Date solved : Tuesday, January 28, 2025 at 07:55:08 AM
CAS classification : [[_high_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{2}+\cos \left (x \right )-2 \sin \left (x \right )+5 x +3 \]

✓ Solution by Mathematica

Time used: 60.022 (sec). Leaf size: 88

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

\[ y(x)\to x \left (-\int _1^0(-\cos (K[1])+2 \sin (K[1])+1)dK[1]\right )+\int _1^x\int _1^{K[2]}(-\cos (K[1])+2 \sin (K[1])+1)dK[1]dK[2]-\int _1^0\int _1^{K[2]}(-\cos (K[1])+2 \sin (K[1])+1)dK[1]dK[2]+3 x+4 \]