2y" + y' + 2y = H(t – 5), y(0) = 0, y'(0) = 0 %3D %3D

Q: y(ln x – In y) dx = (x ln x – x In y – y) dy %3D - -

A: This is the question of differential equations.

Q: y(x+ y)dx + (x +2y – 1)dy = 0 (determination of integrating factor)

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Q: 2y(x² – y + x}&x + (x² –2y)dy = 0 2. Determination of integrating factors:

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Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: 1. Integrating factors found by inspection: (xy + xy)dx+(x²y²-2)dy = 0

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Q: The order and degree of the differential d³y V dy equation: 7+ i. - dx3 dx 3, 2 7,3, 3, 1 3, 7

A: The order of a differential equation is the highest order of the derivative that is present in that…

Q: 1. Integrating Factors Found by Inspection: y(x + y'exy)dx + x(y'exy - x)dy + = 0 when y(0)

A: y(x+y3 exy)dx + x(y3exy-x)dy=0xy dx -x2 dy +y3[x exydy+yexydx]=0xy3ydx-xdy+[x exydy+yexydx] =0xyy dx…

Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

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Q: dy = 3. dt dz at (x, y) = (3, 1) and z² = x² + y² if dx = 1 and dt Find dz Preview dt

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Q: integral of (y^2-14y+5) / y(y-1)(y-5) dy

A: ∫y2-14y+5yy-1y-5dySubstitute u = y-1=∫y2-14y+5yy-1y-5dyApply the Sum Rule:…

Q: y= Iry %3D y (0) = 0 Show that the Ivp has aunique 1T D-1(tッ))っ昇くt っ y<」 Solution - I

A: See the attachment

Q: ) oe.no dy en x = 0-1 of the IVP = x² +y, y(0) = 1 %3D %3D dx s method. Iving the

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Q: y∅=1/(xy^3) is the integrating factor of x^2y^3+(1+y^2)dy/dx=0

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Q: cos(x + y)dx + (3y ^ 2 + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: We have to solve the initial value problem cos(x+y)dx+(3y2+2y+cos(x+y))dy=0 with the boundary…

Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: determination

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Q: Determination of integrating factors: 2y(x² – y + xdx+ (x² – 2y}dy = 0

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Q: . The integrating factor of (4xy+3y2-x)dx + (x+2y)dy = 0

A: Given that: (4xy+3y2-x)dx+(x+2y)dy=0

Q: ar systems of differential eq + 2y = sint x - y' = cost x(0) = 0

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Q: dy Kutta method to integrate = 4e0.8x step size of h 0.5 and an initial condition of y = 2 at x =0…

A: 4th order Runge-Kutta method…

Q: The order and degree of the differential d³y V dy equation: 7+ is dr3 dx 3,2 7, 3, 3, 1 3,7 Question…

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Q: 5. = 2y – 1 dx Solution: = = 2y – 1 (Multiply both sides by dx) = dy = (2y– 1)dx (Divide both sides…

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx - (x +…

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Q: 3. The function 0(x) = 1/ sin(x) is an integrating factor of (ysin(x) + cos(x))dx + (x+ y) sin(x) dy…

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Q: In(y²) dy 3y

A: Given- To do- Evaluate the integral by substitution method.

Q: dx -- 2 = 3y - 2 when x = 1, y = 1 dy

A: the given differential equation is: ydxdy-2=3y2-2 it is given that when x=1,y=1 we have to find…

Q: Determine the Integrating factor of the DE: y (x³e*y y) dx + x (y + x³e*y) dy 3 1

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Q: X ( CSC ( X ) - Y Inx- X y - y dx + x dy = 0 dy - (Iny - Xdx X

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Q: Is 1(y^2) is the integrating factor of the non-exact DE[(y^2)-y]dx+xdy=0, show your solution.

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with  so here we…

Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: 1. dy ==2(y+1);=3y-x+e³; t=0; x = 1;y=1 dt dx dt

A: SOLUTION: Given: dxdt=2(y+1)   ;  t=0;x=1;y=1dydt=3y-x+e-3t

Q: Using separation Variable. 1.) In x dx/dy = 2 / xy^3

A: Given differential equation lnxdxdy=2xy3

Q: y(x + y)dx + (x+ 2y - 1)dy 0 (determination of integrating factor)

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Q: find a sets of solution. Integrating Factors found by inspection   x(x²−y² - x)dx− y(x²−y²)dy= 0…

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Q: Integrating factor for xy dx + (2x2 + 3y2 - 20) dy = 0

A: topic - integrating factor of differential equations

Q: olve for the general solution of the given DE by using the integrating (x³ + xy2 + y)dx + (y3 + x²y…

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Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: Find the integrating factor. (y-xy^2 )dx+(x+x^2 y^2 )dy=0

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Q: Find the integrating factor: (2x^2+y)dx+(x^2 y-x)dy=0

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Q: 2) (2x + sin x) dx + x cos y dy = 0 3) - 2y + a = 0 dx dy 3y 4) r2 (Exact). (Separation variables).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: From an integral equation corresponding to the diffrential equation d'y +x + y = 0 with the initial…

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Q: (x – y ln y + y ln æ)dx + x(ln y– In x)dy = 0 - - %3D

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Q: 5. y(x + y)dx + (r+ 2y – 1)dy = 0 (determination of integrating facto

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Q: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

Q: 7. The integrating factor of the non-exact DE ydx- xdy3D0 is -1/(xy). 8. The integrating factor of…

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Q: ii- (x* + y) dx - ry dy = 0, y(2) = 1 (using Integrating Factors)

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: B. Integration by Parts 1. xcosx dx

A: We know that integration by part formula is given as  ∫uv dx = u∫vdx - ∫dudx∫vdxdx To evaluate: ∫x…

Q: y∅=y^-2 is the integrating factor of 2y(x+y+2)dx+y^2-x^2-4x-1)dy=0

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