1. Solve the fourth-order homogeneous linear ODE:y^(4) − 5y′′ + 4y = 0 2. Determine the values of k for which the equationy′′ + ky′ + (k^2 − 1)y = 0
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1. Solve the fourth-order homogeneous linear ODE:
y^(4) − 5y′′ + 4y = 0
2. Determine the values of k for which the equation
y′′ + ky′ + (k^2 − 1)y = 0
Step by step
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- Find the solution of the following linear ODE given that y(5)=3. Зу dy - (х-4)? dх х-4solve the ODE using the Method of Undetermined Ур and then state y = y + yp. 10x² +9x-9 Coefficients. Clearly label Ye and 1. Solve y" + 6y' + 5y 2. Solve y" + 4y' - 5y = 8ex =solve the ODE using the Method of Undetermined Coefficients. Clearly label y, and y, and then state y = y₁+Yp. Ур Ус Yc+Yp• 2. Solve y" + 4y' - 5y = 8ex
- State the order of the given ODE. Determine whether the equation is linear or linear. Also explain why it is linear or nonlinear. d²y а. dx? + ey. dx dy x3 b. y""+ 4y"+ sinxy' = xy + cos(x) с. у" — 2х(у") +у %3D 3 d*p d. dt4 k p2 e. * - (1-) i + x = 0Determine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * ANSWER CORRECT :|y − x| = C|y + x|3 Any different answer will be considered wrongDetermine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * ** Answer correct :|y − x| = C|y + x|3 ** The answer |y − x| = C|y + 3x|5 is considered wrong
- Determine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * >>>>>>>>>** ANSWER CORRECT :|y − x| = C|y + x|3 **<<<<<< *****The answer |y − x| = C|y + 3x|5 is considered wrong ( will not be accepted as it will be considered wrong)*****Eliminate the Arbitrary Constant: y = c,e* + c2xe* а. y'— 2y" + 2у %3D 0 b. y" - 2y' + у %3D0 с. у' — 2у" + у %3D 0 d. y' – 2y" + 2y = 0 e. none of theseIf a second-order, homogeneous ODE with constant coefficients has a solution y c₁e-5x + c₂e²x, find the ODE. =