The complementary function(C.F.) of the differential equation (D – 7)°(D+ 3)y = 7x is - O (c1 + C2x)e¯ª + c3e³« O (c1 + C2x)e-7* + C3e° O (c1 + C2x)e7* + cze-3* -3x O (c1 + C2x)e"¤ + Cze³*

Q: The complementary function(C.F.) of the differential equation(D – 8)°y = sin 8x is (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Verify that the indicated function y = g(x) is an explicit solution of the given first-order…

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Q: Find the solution of the differential equation (D° + 8D³ + 16D)y = 0 у %3D С, + (С, + C;x)сos y = C,…

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Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+36y=0 Oy"-5y'-16y=0 Oy"-5y'-36y=0…

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Q: Which of the following is the general solution of the differential equation y (iv) +21y"-100y=0? O…

A: We will find out the required solution.

Q: The solution of the differential equation dy dx 2x+12 is 2y-9 O y? – x? = C - O y – 9y – x² – 12x =…

A: Solve by variable separable form

Q: Which of the following is the transformed form of the 2y = x(y')³ – (y')² +1 differential equation…

A: We have 2y=xy'3-y'2+1 Now , differentiate both sides with respect to x:…

Q: Show that each of the functions defined in (A) is a solution of the corresponding differential…

A: To check the solution first check order of Differential Equation and no. Of arbitrary constant in…

Q: The differential equation of y = 5bx2 + c after elimination of the arbitrary constant b, c is O y =…

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Q: Which of the following is the solution to the differential equation dydx=y2−(xy)2dydx=y2−(xy)2 with…

A: Explanation and solutions is given below....

Q: The complementary function(C.F.) of the differential equation(D - 5)y= cos 5æ is_ O (ci + c2a –…

A: Given that  (D-5)^3y=cos5x  To find the complementary function

Q: The Complementary Function of the differential equation (D² – 7D + 12)y= x² cos 3x is O CF = Ae 4x +…

A: first equate D^2-7D+12=0

Q: The complementary function(C.F.) of the differential equation (D² + 6D+18)y=x is_ -37 (c1 cos 3x +…

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Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Find the differential equation of the following function (x – 3y + 2)dx + 3(x + 3y – 4)dy = 0 x-1 a.…

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Q: Determine if the differential equation y'=x4y - 9x5y is separable, and if so, separate it. dy Yes,…

A: Take y common from RHS

Q: A(if both statements are true), B(if the 1st statement is true but the 2nd is false), C(if the 1st…

A: We have to check whether the given both statement are true or false. Definition of order of PDE:-…

Q: Determine the solution of the differential equation y" – 2y' + y = %3D - 1+x2 y = C,ex + C2xe* +÷e*…

A: This is non homogeneous equation of second order so using the method of variation of parameter we…

Q: Form the differential equation for the function 2xy asin2x-bcos2x O a xy" -2y = -4y Ob.xy" + 2y=…

A: Using the product rule of differentiation it can be written that ddx(xy)=y+xdydx . The derivative of…

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

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Q: The general solution of the differential equation x²y" - 2y = Inx is O c,x? + c2xl + 2 lnx - 1…

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Q: Two linearly independent solutions of the differential equation y" - 6y' + 25y = 0 are O yn = e3x,…

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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

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Q: If r1 and r2 are the roots of the characteristic equation of the differential equation y′′−y′−6y=0,…

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Q: Find the differential equation of the following function (x – 3y + 2)dx + 3(x+ 3y – 4)dy = 0 x-1 a.…

A: The given differential equation is x-3y+2dx+3x+3y-4dy=0.....(1) We shall solve the differential…

Q: The auxiliary equation of a non-homogeneous differential equation has complex and distinct roots.…

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Q: The solution of the differential equation 7+ x² + x²y+ 7y 1+ Y dy using variable dx separable x2 Py…

A: Separate the variables from terms of right hand side then transfer the terms of y to the side of dy…

Q: The general solution to the differential equation - 2 ()- is dr = 0 is | dt3 dt2 dt O x = C1 + C2e +…

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Q: Find the general solution of the given higher-order differential equation. d* y dx 7d -18y = 0 dx2 O…

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

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Q: The differential equation formed by eliminating arbitrary constants a and b : y = ax + bx + 13 is O…

A: A. y''  = 0

Q: Find a differential equation whose general solution is y = cje" + c2e¯. %3D О У - 12у - 27у 3D0 O y"…

A: we are given the solution of the differential equation as  y=c1e9t+c2e-3t

Q: 8. Find the solution of the differential equation (D* - 2D +D )y = 0 y = c, + C,x + e*(C, + y = c, +…

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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: If yH of a differential equation is cje2* + cze3x + cze-3x, then W1 = %3D (a) 0 (b) 9 (c) 5e-* (d)…

A: If yH of a differential equation is c1e2x+c2e3x+c3e-3x, then we have to find the Wronskain W.

Q: Determine the solution of the differential equation 2y"-3y'+ 4y = 0 %3D 3X V23 V23 y = e (C, cos x+…

A: Let's find.

Q: State the order of the given ordinary differential equation. d³y dy 4 + y = 0 dx dx3 Determine…

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Q: Using D-operators, the differential equation y"-xy'+ 2y – cos 5x can be written as: A (2D?– xD…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Transform the differential equation xy" - 2y' + Axy = 0, into a Sturm-Linville differential equation…

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Q: 5. In the differential equation, (D³ – 2D² – 3D)y = 0; assume a. y, = A + Be¬* + Ce3* b. y, = A +…

A: This question is based on solution of complementary function.

Q: Solve the differential equation dy dx 9xy - 2y² 6x² xy O a. 3y³ O b. 3x³ x²y = 2y² x²y = 2y² O c.…

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Q: The differential equation for y = Ae3 + Be9r is: %3D o y'+12y'+27y=0 o y'-12y'+27y=0 o y"-12y'-27y=0…

A: Differentiate given equation twice w r to x

Q: Form the differential equation for the function xy ax2 + 2bx-c O a. xy" + 3y" 0 O b. xy" - y" 0 O c.…

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

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Q: The differential equation formed by eliminating arbitrary constants a ,b and c: y= ax³ + bx+ cx +7…

A: y = ax³ + bx + cx + 7 So, y' = 3ax² + b + c  So, y" = 6ax  So, y''' = 6a

Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+16y=0 Oy"-5y'-16y=0 Oy"+5y'+36y=0…

A: Find DE

Q: Verify that y = e3x cos 2x is a solution of the differential equation y"-6y +13y = 0.

A: We have to show that y is the solution of given differential equation

Q: Verify that the indicated function y = P(x) is an explicit solution of the given first-order…

A: Given: y'=2xy2 and y=116-x2