4.45 Problems 2201 to 2250

   4.45.1 \(4 x^3 y'''(x)+x y'(x)-y(x)=0\)
   4.45.2 \((1-2 x)^3 y'''(x)+(1-2 x) y'(x)+2 y(x)=0\)
   4.45.3 \(x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )\)
   4.45.4 \(x^4 y'''(x)+2 x^3 y''(x)-x^2 y'(x)+x y(x)=1\)
   4.45.5 \(\left (x^2+1\right ) x^2 y'''(x)+8 x^3 y''(x)+10 x^2 y'(x)=3 x^2+2 x^2 \log (x)-1\)
   4.45.6 \((x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0\)
   4.45.7 \(4 x^4 y'''(x)-4 x^3 y''(x)+4 x^2 y'(x)=1\)
   4.45.8 \(\left (x^2+1\right ) x^3 y'''(x)-2 \left (2 x^2+1\right ) x^2 y''(x)+2 \left (5 x^2+2\right ) x y'(x)-4 \left (3 x^2+1\right ) y(x)=0\)
   4.45.9 \((a-x)^3 (b-x)^3 y'''(x)=c y(x)\)
   4.45.10 \((x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0\)
   4.45.11 \(y''''(x)=0\)
   4.45.12 \(y''''(x)=x \cos (x)\)
   4.45.13 \(y''''(x)+4 e^{-x} \cos (x)=0\)
   4.45.14 \(y''''(x)=y(x)+\cos (x)\)
   4.45.15 \(y''''(x)=y(x)+e^x \cos (x)\)
   4.45.16 \(y''''(x)+a y(x)=0\)
   4.45.17 \(y''''(x)=a^4 y(x)+x^3\)
   4.45.18 \(y''''(x)+y''(x)+y(x)=0\)
   4.45.19 \(y''''(x)+2 y''(x)+y(x)=0\)
   4.45.20 \(y''''(x)-2 y''(x)+y(x)=0\)
   4.45.21 \(y''''(x)+2 y''(x)+y(x)=\cos (x)\)
   4.45.22 \(y''''(x)-2 y''(x)+y(x)=\cos (x)\)
   4.45.23 \(y''''(x)+2 y''(x)+y(x)=24 x \sin (x)\)
   4.45.24 \(y''''(x)-2 y''(x)+y(x)=e^x+4\)
   4.45.25 \(y''''(x)-2 y''(x)-8 y(x)=0\)
   4.45.26 \(y''''(x)+3 y''(x)-4 y(x)=0\)
   4.45.27 \(y''''(x)+5 y''(x)+6 y(x)=0\)
   4.45.28 \(y''''(x)-12 y''(x)+27 y(x)=0\)
   4.45.29 \(y''''(x)+a^2 y''(x)=0\)
   4.45.30 \(y''''(x)+a^4 y(x)+2 a^2 y''(x)=0\)
   4.45.31 \(y''''(x)+a^4 y(x)+2 a^2 y''(x)=\cosh (a x)\)
   4.45.32 \(y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)=0\)
   4.45.33 \(y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0\)
   4.45.34 \(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=0\)
   4.45.35 \(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x}\)
   4.45.36 \(-2 y'''(x)+y''''(x)+y(x)^2=0\)
   4.45.37 \(-2 y'''(x)+y''''(x)+y(x)^2=x^3\)
   4.45.38 \(2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0\)
   4.45.39 \(-2 y'''(x)+y''''(x)+2 y''(x)-2 y'(x)+y(x)=0\)
   4.45.40 \(2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0\)
   4.45.41 \(2 y'''(x)+y''''(x)-3 y''(x)-4 y'(x)+4 y(x)=0\)
   4.45.42 \(-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0\)
   4.45.43 \(-4 y'''(x)+y''''(x)+6 y''(x)-4 y'(x)+y(x)=0\)
   4.45.44 \(-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0\)
   4.45.45 \(4 a x y'''(x)+y''''(x)+a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)=0\)
   4.45.46 \(2 \left (y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)\right )=\cos (a x)+\cos (b x)\)
   4.45.47 \(-12 y'''(x)+4 y''''(x)+11 y''(x)-3 y'(x)=0\)
   4.45.48 \(3 y'''(x)+x y''''(x)=0\)
   4.45.49 \(5 y'''(x)+x y''''(x)=0\)
   4.45.50 \(x^2 y''''(x)=2 y'''(x)\)