1- y"+y'-2y = x² + e³x what is the particular (nonhomogenous) solution of the given ode? OA) Y = Asin x + B cos x 3x OB) Yp=e³ (Acos x + B sin x) Oo yp = ax² +bx+c+De³x OD) Yp = e³x OE) Y₂ = ax+b+Ce³x

Q: Solve the following ODE c) y' + (cos x)y = cos x (1st order) d) y' +y = -2xy2 (Bernoulli Method)

A:

Q: 1) Solve the ODE below. a) x²y" - 3xy' = x²

A: According to Bartleby guidelines I have solved first, since this is not interrelated question,   For…

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

A:

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

A: Given differential equation We have to find the solution of the differential equation.

Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: Find the solution of x²y" +5xy' +(4+4x)y=0, x > 0 of the form n =1,2,3,... where co 1. Enter r = =…

A:

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

A:

Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: Question 2 Obtain G.S. X- y tan y =)] O dx + x tan O Lnx + Ln sec x dx = C Lnx + x tan-¹x 16 X 1+x²…

A:

Q: |(5e" + 5x4 =. + 9 cos x)dx 5et + x + 9 sin x + c 5ea + x + 9 cos x + c 5e + x³ – 9 sin x + c O et –…

A: Need to find integration

Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

A:

Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

A:

Q: on of y" – 2y' + 2y =

A:

Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: Find dy dx 1) y = -1/323 ; tan 43 2 y = sec 5x 3) y = cos cos 2x + tan¹ \/ / 4) y = cot²¹ 2² 2 5) =…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: uesuon o of 8 Determine the general solution (du/dt)3-(du/ dt) "2-2u = Select the correct response…

A:

Q: The values of C₁and C₂ so that y(x) = C₁ sin x + C₂ cos x satisfies the following conditions; y(0) =…

A: Here we have to find the value of c1 and c2 using given conditions.

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: نقطتان )2( What is the Form of the General * ?Solution for this equation A. y(x) = Aem; + Bem;x dy?…

A: Given,  dy2dx2+dydx-6y=0

Q: Give the form of a particular solution of yl4) + 2 y " + 10 y "+ 18 y '+9y =5 e+ cos(x) +4 given…

A:

Q: (4e® + 4x° + 8 cos x)dx 3 O 4e" + x4 + 8 cos x + c et – x4 + cos x + c et + x4 – 8 sin x + c O 4e" +…

A:

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

A:

Q: (5e + 4r +4 cos z)dr = O e – r + cos z +c O e +r - 4 sin z +c O 5e + r - 4 sin z +c O 5e* + x +…

A: The given integral is: ∫(5ex+4x3+4cos x)dx

Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

A:

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

A:

Q: Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact? A)…

A:

Q: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

A:

Q: Find the general solution of y'"''- 6y'"+2ly'– 26y=0 A y=c,e-+cze* cos 2x + c,e*sin 2r ® y=c,e+c,e…

A:

Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

A:

Q: By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form:

A: Bernoulli ODE:         "An ordinary differential equation is called a Bernoulli differential…