(D² -9)y = e* (D² -5D+6)y = es y"-9y'+2y =x 3x ii) (D'-9hy=e* o (6:-SD+6y=e" iv) vi) 3x %3D y"-7y'+12y=x (D-3)'y=e* (D-3)y=e* viii) (D+3)°y= er (D+3)° y = e3* (D+3) y = xe* x) (D-2)y= xe* xii) -3x

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A:

Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

A:

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: (1) Find the general solution for -) dx - -) dy = %3D

A:

Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

A:

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

A:

Q: 2. Identify the 3rd order nonlinear DE. 3 (dy` A. ( +x³y – xy³ = 0 dx. d³y d²y +y dx2 В. = 0 dx3 d³y…

A: Check each options while it is 3rd order as well as nonlinear differential equation.

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

A:

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

A:

Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

A:

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D…

A: solution

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

A:

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: 4+2x If g(x.y) = By then the mixed partial derivative at the point (- 2. is:

A:

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

A:

Q: (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy-5yzª dz

A: Find the value of function using integrate Compare the given expression with Mdx+Ndy+Pdz to obtain…

Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

A:

Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

A:

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

A:

Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

A:

Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

A:

Q: Show X -メ+1 =ソ- Can be reduce d to homegenons equation 2X +y-! メ+ 2y t1 dy dx

A:

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

A:

Q: 3. f sin³y(2-3cosy)² dy

A:

Q: Solve for y + In lyl at x=6: y'=(yx^2-y)/(y+1); y(3) = -1 4.5

A: The given differential equation is y' = y x2 - yy +1  with initial condition y ( 3 ) = -1. To solve…

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

A:

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: Compute both dy/dx and d^2y/dx^2 if x^3 + y^3 = x.

A:

Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

A:

Q: Find both first partial derivatives. z = 10y² Vx Oz dz %3D %3D

A:

Q: 4. (4y+ 21 - 5)dt +(6y+41 –1)dy = 0, y(-1)= 2 cs

A:

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

A:

Q: Find at x = -2 if y = - 4x² + 3 and dy dt dy dt = dx dt - 1.

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.