Verify that the expression: 1 C(t,T) = 1 e-b(T-t) 1 + ab -a(T-t) a(a – b) b(a – b) is the solution to the differential equation: 1 — е-а(Т-t) C:(t, T) + - bC(t, T) = 0

Q: Verify that the general solution satisfies the differential equation                     y = Ce−6x,…

A: General solution is, Differentiating with respect to x, we get

Q: Show that the y,(2) = K, (1 – 2x* +*-*-)* * (2x -+ 4 x6 + ... 45 4 + K2 (2x 4 8 + ... 3 15 315 is…

A: we have given yh(x)=k11-2x2+23x4-445x6+...+k22x-43x3+415x5-...is complementary solution of…

Q: Convert the differential equation u' – 5u' + 5u = e“ into a system of first order equations by…

A: Given differential equation is u''−5u'+5u=e4t......1 We have to write the given differential…

Q: Verify that y(t) = t and y2(t) differential equation ty" - 2y = 0 for t > 0. Then show that y = cyt…

A:

Q: c. x²y″ − 3xy' +4y=0, _y(1)=5, y′(1)=3. - - d. x²y" — 5xy' + 8y =8x6, y(½)=0, y′(½¹⁄) = 0.

A: (c) A differential equation is given by, x2y''-3xy'+4y = 0 with initial conditions y1 = 5 and y'1 =…

Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: When solution of any differential equation is given, then substitute the solution into the equation…

Q: Determine the constant A such that the differential equation (Ax²y + 2y²)dx + (x³ + 4xy)dy = 0 is…

A:

Q: Prove that if f(x) solves a linear homogeneous differential equation with constant coef- ficients…

A:

Q: Show that if a, b, and c are positive constants, then all solutions ofthe homogeneous differential…

A:

Q: (b) Write the general solution of the homogeneous linear differential equation of order 4 for which…

A:

Q: Verify that the function y = C1ex + C2e2x is a solution of the differential equation y" - 3y' + 2y =…

A: The solution of a differential equation must satisfy the differential equation. It is known that:…

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A:

Q: Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe…

A:

Q: (b) Use the superposition approach to solve the non-homogeneous differential equation, y" + 6y' + 8y…

A:

Q: Solve the differential equation using Reduction of Order (D² + 2D + 1)y = (e* – 1)-2

A:

Q: y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2

A:

Q: 3. Determine the solution of the differential equation +-y x3 given that y (1) A ax +R

A:

Q: / solve the differential equation by the Laplace: (One only) 1- y" - 3y' + 2y = 4e2t y(0) = -3 ,…

A: As per our guidelines we are supposed to answer one question only. For the solution of the question…

Q: Find a suitable form for particular solution of the differential equation y" - 4y' + 13y te"…

A: 1st is correct answer see the solution on step 2

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

A:

Q: Show that the functions x, x2, form an FSS for the differential equation x³y" +x2y" - 2xy' +2y = 0.…

A:

Q: V29. Verify that the piecewise-defined function (-, x<0 y = 2, x 0 is a solution of the differential…

A: As per the company's guidelines, we are suppose to answer the first question. Kindly repost the…

Q: The differential equation, (x + 3y - 5) dx - (3x + y - 7) dy = 0 can be transformed into homogeneous…

A:

Q: Which is the particular solution of the differential equation y"+ p(z)y'+ g(z)y--2z which has two…

A: Given differential equation y''+pxy'+qxy=−2x Given that x4 and x-3 are the solution of the…

Q: Solve the differential equation by eliminating the arbitrary constants. Choose the right answer from…

A:

Q: Determine whether the differential equation (5.a2 – 2xy + 4) dr + (2y² – x² + 5) dy = 0 - is exact.…

A: The given differential equation is 5x2-2xy+4dx+2y2-x2+5dy=0

Q: Consider the differential equation x²y" - 7xy' + 15y = 0; x³, x5, (0, ∞). Verify that the given…

A:

Q: (b) Use the substitution a e' to transform the Cauchy-Euler equation a*y" – 4xy' + 6y = 3x + In(a"),…

A:

Q: Which term is included in the solution of the differential equation у" — 2у' - Зу — е" , у(0) — 1,…

A:

Q: Form the Differential equation if its solution is V=acos(2x +b) O a. y'= 2x b. None of these O c.…

A:

Q: Show that y = Vx],(Ax), 1> 0 is the solution of the differential equation %3D x*y" + (x²x² – v² +±)…

A: The given differential equation is,  x2y''x+λ2x2-v2+14yx=0 This differential equation can be written…

Q: Consider the differential equation: (5x – 1)'y" (x) + 3(5x – 1)y(x) + y(x) = 9(5x - 1)-1 (1) a)…

A: The given differential equation is the Cauchy Euler differential equation.  To find the solution we…

Q: Verify that y1 = x and y2 = xe" are solutions of the differential equation x²yll – x(x + 2)y! + (x +…

A:

Q: Consider the differential equation x²y" - 7xy' + 15y = 0; x³, x5, (0, co). Verify that the given…

A:

Q: To reduce the differential equation with linear coefficients (x+2y-4)dx - (2x+y-5)dy = 0 to a DE…

A:

Q: Which term is included in the solution of the differential equation y” - 2y’ - 3y = e^x , y(0) = 1,…

A: Given differential equation y” - 2y’ - 3y = e^x , y(0) = 1, y’(0) = 1

Q: Use order reduction to find the solution of the differential equation. 4x²y"+y= 0; y, = x² In x 1/2

A: Let y1(x) be non-trivial solution of differential equation y''+p(x)y'+q(x)y=0 and let…

Q: 5. Verify that the general solution y= Gx + C,x³ satisfies the differential equation x?y" – 3xy' +…

A: y=C1x+C2x3Differentiate w.r.t. 'x'y'=C1+3C2x2Differentiate againy''=6C2xPut these values in…

Q: . Verify that the functions y1(x) = 1, y2(x) solutions of the differential equation xy" – y" = 0 on…

A: Given information: Differential equation xy'''-y''=0 An Euler homogeneous ODE is a form of…

Q: Consider the differential equation x²y" - 4xy' + 6y = 0; Verify that the given functions form Form…

A:

Q: Consider the differential equation x²y" - 7xy' + 15y = 0; x³, x³, (0, 00). Verify that the given…

A:

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation as v"x=5x2

Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

A:

Q: Find the general solution of the second-order linear homogeneous differential equation with constant…

A:

Q: (a) Solve the Cauchy-Euler equation solution of the differential equation a*y" – 3ry' + 13y = 0, r >…

A:

Q: Consider the differential equation: (5.x – 1)°y"(x) + 3(5x – 1)y (x) + y(x) = 9(5x – 1)- (1) a)…

A: We have to show that the given differential equation becomes the differential equation…

Q: 5. Verify that the indicated pair of functions is a solution of the given differential equation on…

A: We need to verify that given pair of function is a solution of the given system of differential…

Q: A. Obtain the differential equation of the gi- (1) 3x² – xy² = c (2) y = a cos(x +B) (3) y = c,e¬2x…

A:

Q: Prove that x = 0 is a regular singular point of the given differential equation, then find the first…

A:

Q: Find the general solution to the differential equation: 3y[In(x)] - 2xy' = 0 for x,y # 0 %3D

A: