6. y = xe* 7. y= 3x.e* 8. y = x² In(x) 9. y =x*(5x – 1) 10. y = (x² + 2x)5(3x-3 +x²)-7 11. y = (1 – x³)e²* 12. f(x) = x²e-6x 13. y = 2x°(1+x)5 14. y = x²(1+ x) ,2x %3D %3D

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

A:

Q: What is the solution to the initial value problem y" – 2y' + 10y = 0, y(0) = 3, y'(0) = 0 ? A) y =…

A: To find The solution to the given initial value problem .

Q: dx 5x cos(3t) dt with x(0) = -4.

A:

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

A:

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: 4. Find the General and Particular solution of dy -8 sin 4x ; y = 6 when x = 0 dx dy

A:

Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: Solve the initial value problem. 33) dy - et sin (et – 5), y(ln 5) = 0 dt A) y = sin et - sin 2 C) y…

A: Given initial value problem can be evaluated as shown below by using substitution method

Q: Solve the diffevential cauationm. du e cosn=0,0 X2015,40)-a. Alam - Moislton method with h=0.4.

A: The given differential equation is, dydx+y-e-xcosx=0

Q: ду 9. The differential equation (3ycos.x+4xe" +2x'e" dx+3(sin x+1)dy 0 is exact because ON 10. The…

A:

Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

A:

Q: 1- Problem 4: B) Estimate the following integration with n = 4 using Trapezoidal rule and find the…

A:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: Solve the initial value problem: y'+2y = 40sin(t)+cos(t),      y(0)=6

A: Given,y'+2y = 40sin(t) +cos(t)y(O)=6

Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = + 10e',…

A:

Q: 1 So 2t en + e-2t ezt - e-at dt

A:

Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

A:

Q: Find the largest interval in which the solution of the initial value problem y" + csc(t) y' +…

A:

Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

A:

Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it…

A: The two-dimensional heat equation is given by The steady-state heat equation without a heat source…

Q: Show that f(x, y) = e2x cos(x + In y) satisfies the differential equation 2f - yfyx = 5f.

A: Given that fx,y=e2xcosx+lnyShow that 2fx-yfyx=5f

Q: Find the largest t-interval where the solution to the IVP (t − 5)y'' - cos(t)y' + y = 2/t,  y(1) =…

A: Consider the provided question,

Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

A:

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

A:

Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

A:

Q: Without solving for the undetermined coefficients, the correct form of a particular solution of the…

A:

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

A:

Q: 3- Find non-zedo solution ofs dy

A: we need to solve the given first order nonlinear differential equation. The given equation is…

Q: 2 2 x+y e to pday dyd x |-X

A:

Q: Suppose that x = 0 is a regular singular point of the differential equation x²y" – x(x + 3)y' + (x +…

A:

Q: 6. Given that y = 0 when x = 1, show that the solution of the differential dy equation 2xy- - = y² +…

A: Answer and explanation is given below....

Q: 4) Let y(x) be the solution of the initial -value problem y' = cos(x + y), y(0) = 0. Use Euler's…

A: To find the solution of initial value problem.

Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

A:

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2(a) Form the partial differential equation from z = ar + by + ab by eliminating the constants a and…

A:

Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

A:

Q: Find solution to hon-homo geneous heat problem ut = Uxx + Cos(HX) ; +70 17X70 u(x,o)= f(x); OLX <I…

A: We will use basic knowledge of PDE theory and analysis to answer this question.

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: Q.2 (a) Form Partial differential equation from z = ax² + by?

A: the given equation is z = ax2 + by2 .......(1)

Q: Apply Euler's method to approximate the solution of the initial value problem y' = 2 cos(2x) cos(y),…

A: We have to find the value of y(2) using Euler's method for approximation.

Q: If we use the Method for Variation of Paramet nonhomogeneous differential equation for wh W, =…

A:

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

A:

Q: The given differential equation is already in standard form, as the coefficient of the highest order…

A: We have to find Wronskians.  Wronskian W(y1, y2) is the  W(y1, y2) = y1y2' − y2y1' Since y1 and y2…

Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…