dy 3x 23. X + (3x + 1)y = e dx

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: 33. Compute the differential equation * + y = 0 when y (0) = 1, y (0) = -1 dx2 O y = 3e* - 2xe* O y…

A: Solution

Q: The solution of the differential equation 3.9 + x² + x²y+ 3.9y 1+ Y dy dx using variable separable y…

A: The given equation is dydx=3.9+x2+x2y+3.9y1+y On simplifying this, we get…

Q: 8. Use a substitution to solve the homogeneous 1st order differential equation (x – y)dx + x dy = 0

A:

Q: 2] The linear differential equation with constant coefficients satisfied by the equation y = 2x 5e2*…

A: Hence option (b) is correct.

Q: 5. The standard form of the first order linear differential equation dy-(cscx-ycotx)dx=0is

A: Given differential equation, dy-cscx-ycotxdx=0 The objective is to find the standard form of the…

Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

A:

Q: (4x3 – 3y²)dx + 6xydy = 0 Ans: 2x3 + 3y² = 2x %3D

A: first will convert the given differential equation into linear differential equation of first order…

Q: 1. The standard form of the general first order linear differential equation in y is 2. The linear…

A:

Q: [6] Find the solution of the first order ordinary differential equation (1– 3y2) dy – x sinx dx=0, y…

A:

Q: Determine the general solution and the particular curve that goes through point (0,0) of the e* cos…

A:

Q: What is the particular solution to the dy dx differential equation initial condition y(-3) = 2? with…

A: here is the solution

Q: 1 xdy – y(1+ y cos 2x)dx = 0 ;y(0): Ans: 2x + y sin 2x = 0 2

A:

Q: 4. Solve the differential equation 2x(2x – 1)- (x + 1)+y = 0 using the method of Frobenius. dx2…

A: 2x2x-1d2ydx2 +x+1dydx +y=0                       eq.(1) To solve by Frobenius series.

Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y" +y' – 2y = x² - x+e*…

A:

Q: 2.) Find an explicit general solution y(x) for the homogeneous differential equation ry = y ln

A:

Q: 3. The differential equation 3y(r -1dx+(x' +8y-3xdy 0; is exact because ам ON

A:

Q: DIFFERENTIAL EQUATION dy/dx=2yx+yx^2

A:

Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

A:

Q: 4. The differential equation (3.y-4y' +6)dx+(x' – 6x?y' -1)dy = 0is exact because %3D aN

A:

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

A:

Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: x+ y, (e* + In y)dx + (dy = 0

A: We have to solve the given first-order differential equation…

Q: 6. By making the change of variables u = and u = y , solve the partial differential equation rfz…

A:

Q: Q3. Second order non-homogeneous ordinary differential equation is given as: y"+ y' – 2y = x² - x+e*

A:

Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

A:

Q: x(1+ y³)dy + ydx = 0 ;y(1) = 1 Ans: In(xy)3 + y3 = 1

A:

Q: Find the general solution of the non-homogeneous differential equation Y” –  2Y’  + Y  =  4 cos x

A:

Q: 2- Find the solution of these differential equations : 1. (x – y) = x + y dy dr

A:

Q: 1. The order of the differential equation 5x- d'y aty + 3x + w'y = 0 is

A:

Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

A:

Q: 3. Given that y = 1 when x=-1, find particular solution to differential equation dx dy – 3x²y² =…

A:

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: 22/ for the differential equation ģ =X+y if ylo)=1 s ind y (ood) by Using Euller modibied method…

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: 19. The differential equation (2xy - y^2+ y) dx + (3x^2 - 4xy + 3x) = 0 is

A:

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

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

Q: 5. The differential equation (3r*e" - 2xktx+(r°e' -sin y}dy = 0 is exact because ƏN ƏM ôx

A:

Q: 20.Find the particular solution of the differential equation x +1) = x3 – 2y, given x = 1 dx when y…

A: We have to find general solution of given differential equation with initial condition.

Q: 2. Find all values of r for which y = e™ is a solution of the second order differential equation y"…

A:

Q: Find the general solution of the higher order linear ordinary differential equation: y"' + 2y" + 4'…

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

Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: For the differential equation (x² – 3)y" + (x+ V3)y' + y = 0, singular point is a regular X=9 x=3…

A: Given