1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos x=0 b. 8ty"-6t²y'+4ty-3t²-0 c. sin(x²)y"-(cosx)y'+x²y = y'-3

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1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos x=0
b. 8ty"-6t²y'+4ty-3t²-0
c. sin(x²)y"-(cosx)y'+x²y = y'-3
d. y"+5xy'-3y = cosy
2. Verify using the principle of Superposition that the following pairs of functions y₁(x) and y2(x) are solutions to the corresponding differential equation.
a. e-2x and e-3x   y" + 5y' +6y=0
3. Determine whether the following pairs of functions are linearly dependent or linearly independent.
a. fi(x) = ex and f(x) = 3e³x
b. fi(x) ex and f2 (x) = 3e*
4. If y(x)=e³x and y2(x)=xe³x are solutions to y" - 6y' +9y = 0, what is the general solution?
1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the
equation is linear, determine further whether it is homogeneous or nonhomogeneous.
a. (cosx)y"-siny'+(sinx)y-cos x=0
b. 8ty"-6t'y'+4ty-3t²=0
c. sin(x*)y"-(cosx)y'+x°y = y'-3
d. y"+5xy'-3y = cosy
2. Verify using the principle of Superposition that the following pairs of functions y1(x) and y2(x) are
solutions to the corresponding differential equation.
а.
e-2x and e-3x
у" + 5y' + 6у %3D0
3. Determine whether the following pairs of functions are linearly dependent or linearly
independent.
a. f1(x) = e* and f2(x) = 3e3x
b. f1(x) = e* and f2 (x) = 3e*
4. If y1(x)=e3x and y2(x)=xe³* are solutions to y" - 6y' + 9y = 0, what is the general solution?
Transcribed Image Text:1. Classify each of the following equations as linear or nonlinear (explain you're the reason). If the equation is linear, determine further whether it is homogeneous or nonhomogeneous. a. (cosx)y"-siny'+(sinx)y-cos x=0 b. 8ty"-6t'y'+4ty-3t²=0 c. sin(x*)y"-(cosx)y'+x°y = y'-3 d. y"+5xy'-3y = cosy 2. Verify using the principle of Superposition that the following pairs of functions y1(x) and y2(x) are solutions to the corresponding differential equation. а. e-2x and e-3x у" + 5y' + 6у %3D0 3. Determine whether the following pairs of functions are linearly dependent or linearly independent. a. f1(x) = e* and f2(x) = 3e3x b. f1(x) = e* and f2 (x) = 3e* 4. If y1(x)=e3x and y2(x)=xe³* are solutions to y" - 6y' + 9y = 0, what is the general solution?
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