rom the homogeneous solution. ty" – 2y = 7t2 – 1, t > 0, yı(t) = t², y2(t) = t¯". %D Enter an ecact answer.

Find a particular equation for the DE: y+4y' - 2y = 2x - 3x +6

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?     Question   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…

Without solving, classify the following equations as to: separable, homogeneous (the degree), exact, linear, Bernoulli, or Ricatti (d) y + 5y? + 2ry = 3r*. %3D dy (e) y dr +r dy - 0. (f) = () y dr = (y- ry²) dy(h) r dy ye/y. - r.

Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

Solve y′′+ 9y = 3sin(3t)

Find the general solution by undetermiend coefficients.

Find General Solution of y" + y" = 0.

Convert the given equation into the form of a Sturm-Liouville equation. y" +7y' + ay = 0 Write the Sturm-Liouville form of the equation, using x as the independent variable.

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