10. Give the general solution of (D3 – 3D -2)y = 0 a. y = ce-* + c2xe¬* + c3e b. y = ce* + c2xe¯* + cze2* c. y = ce¯* + C2xe* + cze2* d. y = cze* + C2xe -2x + cze2* ,2x

Q: 1- If y+3y = 8 then g-solution is %3D a- y+ 6 = 1 In (8-3y) = x +c a.

A:

Q: 17. Find the general solution of* (4D4 + 4D³ – 3D² – 2D + 1)y = 0 y = (Cz' + C)e + (C3a + C4)e" y =…

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Q: Find the solution to the IVP.y = cscx – ycotx' y(÷)= 1 ysinx = x+ 2 ysinx = x + 1- I 2 ycscx = x +…

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Q: Find the general solution of the DE dyldx = (x - y) / (x + y). O y^2 - 2xy – x^2 = C O y^2 + 2xy –…

A: We have to find general solution of  differential equation.

Q: 17. Find the general solution of * (4D + 4D3 - 3D² – 2D+ 1)y = 0 y = (Cr+Ca)et +(Ca + C)e y = (Cr +…

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Q: Discuss the solutions of the system (2)…

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Q: Find a particular solution to y" + 4y + 3y = -8te". %3D Yp

A: Given differential equation is  y"+4y'+3y=-8te2t

Q: If y is a solution of y"+xy'+3y =0 then find the

A: Find y' and y'' from the equation y=∑m=0∞ amxm .                                       y'=∑m=0∞…

Q: The solution of the nonhomogeneous DE y" – 2y' +1 = 3e3x is y = cqe* + c2xe* + 3x y = cqe2x + c2 +…

A: We need to find the solution to the nonhomogeneous DE y''-2y'+1=3e2x⇒y''-2y'=3e2x-1. The…

Q: 8. Obtain the general solution to the equation ( Dª - 3D³ + 5D² - 9D + 6 )y = 0 a. y = cie* + c2e2x…

A: If the roots m1,m2,...,mn of the Auxiliary equations are distinct and real then the complete…

Q: 6. Consider the system: | | dt = 2.r y(8 + 2y) + 2ry

A: Given: Let us consider the given system, dxdt=14xy-2x⇒Fdydt=y8+2y+2xy⇒g

Q: 23. Solve the Cauchy problem 1 (r+ y) uz + (r – y) uy = 1, u (1, y) = %3D

A: Given: x+yux+x-yuy=1 , u1,y=12

Q: dY 4 2 Y. dt 2 1

A: First, find the eigenvalue for the matrix , A=4221 as follows.…

Q: 2 32. The equation of the straight line that corresponds to the null-space of A = -5 is: -4 10 2 (A)…

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Q: 4. Show that 4=3y'z² ¿+4x²:* j+6x°y'% is solenoidal.

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Q: 5. Find the particular solution of D' + 3D° + 2D° ]y=0 provided that when x = 0, y = 0, y' = 4, y" =…

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Q: 7. Find the general solution of ( D5 + 3D4 – 21D³ – 47D² + 120D + 144 )y = 0 a. y = ciex + c2e3x +…

A: To find out the general solution.

Q: Find the general solution to(D5 - 2D³ – 2D2 – 3D - 2)y=0 O y= e-X(C1 + C2x)+ C3e2× + C4cosx+ C5sinx…

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Q: 4 - Find the general solution of y + 3y'+ 2y -e a) y(x) = Cie b) y(x) = Cie 2 + c2e -e c) y(x)= c1e…

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Q: y = 0, is: %3D The general solution of y +xy +9x-4 Oa C,(3x) + C,Y,(3x) Ob C,XJ,(3x) +C,xJ_2(3x) Oc…

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Q: Let f(x,y) = C be the solution of the DE 2e3cos(vin(x)dx-3xsin(y)e3cos(in(x))-dy%3D0, where (x,y)…

A: We need to find value of C.

Q: What is the general solution of (D° + 14D³ + 49D) y = 0 Oy = (C1 + C3z) cos v7a + (C2 + C4x) cos 7z…

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Q: Show that y = In (x) is a solution of xy" + y² = 0.

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Q: 10y" + y" - 7y' + 2y = 0

A: differential equation

Q: Find an actual explicit solution to y'=t/y,y(2)=- O y(t) = -(t^2 - 3)^1/2 O y(t) = -(t^2 - 3) O y(t)…

A: Given query is to find the solution for the differential equation.

Q: Show that u(x, y) = y²e* + 3x² is the solution for u = yuyy + 6x . 2

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Q: What is the general solution of (D3 - 2D² - 5D + 6) y = 0 ? Oy = Ce 2 + Cze + C3ze3z Oy = Ce + Cze2z…

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Q: What is the general solution of (D - 3D- 10D) y 03 Oy = Cie + Cze + C3er Oy = Ce 2 + C2 + C3e Oy =…

A: Given differential equation is linear homogeneous differential equation of first order. First we…

Q: 1. The complementary equation to dt² + dy + 4y = 5e-³t is:

A: Solution is here

Q: The solution to the non-homogeneous DE y' - Бy +ву 3D2х + 3 is 2. a. Ae3x + Be3* +1/3 x + 7/9 b.…

A:

Q: 1. Use operator / elimination method to solve the given system dx dy + = 2x + 2y + 1 dt dt dx dy y +…

A: Since you posted multiple questions, we will solve first question for you.

Q: 3) Show that there are no nonconstant periodic solutions to the following system. x' = x + y + x³ –…

A: Taking β(x,y)=1, and comparing the given system with theorem 7.4, we get x'=x+y+x3-y2=f(x,y) and…

Q: Obtain the genral solution to (D5-15D³+10D² +60D-72)y=0 y=e²x(C₁ + C₂x) + e-³x(C4+C5x) y=e²x(C₁+C₂x…

A: Given differential equation is D5-15D3+10D2+60D-72y = 0

Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

A:

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: (): Suppose y = cjex + czetx is the general solution to y = Ay. What is A %3D %3D ? We don't have…

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Q: Find the general solution to(D5 - 2D3 -2D² – 3D – 2)y=0 O y= e-X(C1 + C2x) + C3e2X + C4cosx + C5sinx…

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Q: 4. Find the general solution of (x3 + y³) dx = 3xy² dy = Cx = Cx А. -Зx3 + 2yз В. 7x3 + 2у3 С. -бх3…

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Q: Find the general solution of y" + 4y' = 0 O a. y= Ce*+ C2cos(2x)+ C3sin(2x) O b. y= C, + C2e-2x +…

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Q: 24- Since D is a square whose vertices have coordinates (0,0), (0.2), (2,0), and (2.2), which of the…

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Q: 3. yl-2y +2y = ecosx %3D

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Q: 3. Find the genesral Solution: y* 5y^ +3y' -ay=

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Q: 2 The general solution of y +xy+ 9x* - 4 y = 0 is: O a C,J,(3x) + C, Y,(3x) Ob. C,xJ,(3x) +…

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Q: 4. Are y1 (x) = e*and y2(x) = x + 1 solutions of the D.E. xy" – (x + 1)y' +y = x2. Are y1(x)…

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Q: 1. Find y by Cramer's rule for the following linear system. x+Oy+2z=6 - 3r+4y+6z=30 -r-2y+3z=8

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Q: 1- If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8-3y) =x + c 3 a

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Q: Find the general solution to (D5-2D3-2D²-3D-2)y=0 O y= e-X(Cı + Czx) + C3e2X + C4COSx+ Cssinx…

A: Sol:- This can be written as :- D5-2D3-2D2-3D-2=0D+12D-2D2+1=0D+1=0  or   D-2=0  or   D2+1=0The…