Ex: Salve the equation ofD-o Pelatermeth dy inzx

Q: b. f(x)dx

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Q: 31x dy-y- -y salve thedifferen tial xP Equation

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Q: dy Solve the following IVP: (x²y + y +5x2 + 5) = y2 + y - 2; y(1) = 2 dx

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Q: Solve the following IVP correctly: x3+y3 dx + 3xy2+y3-2 d'y=O

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Q: I Solve the following FODF (x1)x*dy= (3x3y-xy +y²)dx

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Q: dx If |h(0) de, then h(e) d0 : (4+x²)³

A: Given, ∫dx4+x23=∫hθ dθ

Q: + e sintil dxdydz yz In3 ...b.. dxdydz..Anss. ............ ........... ...

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Q: Solve the following aifferen tial equations |. x* dy = (4x* +5xy +y*) dx 2 2x + y X -24 2. dy dx

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Q: •2 cy sỏ , (xy2 + x) dxdy.

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Q: cos(s) d udu = ds -8

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Q: Solve the following IVP: (x²y+y +5x2 +5)Y =y2 +y-2; y(1)=2 dy dx

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Q: 13. (x? — ху + у?)dх — хуdy %3D 0

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Q: 1 d?y X = 3 ; y = u3 + 3u dx?

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Q: (1 – 2² + y²) dx + (1+x² – y³) dy.

A: Here we combine C1 and C2 and then Apply Green's Theorem.

Q: If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8, 8).

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Q: Y and 2 Y if x dx? 七 and yo

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Q: y²dy = x(xdy – ydx)ey

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Q: Solve the following SLP y" + ly = 0 y(0) = y(1) = 0

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Q: d’y dx? if y = In(cscx)

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Q: ſcsch¯(1– x¯)dx

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Q: (ху + х)dx — (х?у? + х? + у2 +1)dy 3D 0 |

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Q: d² y If ax? dx? 3. Find + 2 hxy + by = 1, h? - ab Ans. (hx + by)

A: So in this we have to differentiate twice. I'm providing hand written solution.

Q: (22 + y? +1) dæ + x (x – 2y) dy = 0

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Q: dy et-y dx 2.

A: The given problem is to solve the given differential equation using separation of variables method.

Q: Solve by integrating factor by inspection: * 2 ydx — 3хy? dx — хӑу %3D 0

A: Explanation of the answer is as follows

Q: If h(2) = 6 and h'(2) = −8, find d/dx (h(x)/x) | x=2

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Q: Given: f(x, y) = x³y – y cosh xy Solve for D132

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Q: SS5x²cos(xy)dxdy 1-

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Q: Solve following diffrential equation x(dy/dx)+6y=9x^2

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Q: •3 2ye dx dy y? Evaluate

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Q: Find d?y/dx2 for the following equations: e) xy + y2 = 1

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. If = 2xy, and y(- 1) = 2, find y(2). dx 3 А. 4e 3 В. — 4е' C. 3 С. 2 2 D. 5 E. - 4

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Q: (2x² – ye")dx – et dy = 0.

A: Consider the differential equation  2x2−yexdx−exdy=0

Q: 1 1. X CasCx y) dxdy. 0.

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Q: 3- Solution of the following equation * dy 2 d?x = 2(3+ x2 - xy)/x³ dx

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Q: | y(y? + 1)5 dy

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Q: Find dx d'y , if x=t-r and y=t-t.

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Q: 2). EX+1 3t1a4 14. 13 What is the value of EX+1 for scoves I,

A: Given X1=1 X2=6 X2=3

Q: If h(2) = 5 and h'(2) = −8, find d dx   h(x) x       x = 2.

A: Given:

Q: ye'xdx (4 + e?x)dy

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Q: Solve 1Ge follouing disferential eguatiug 2 dy ty= elx xy メー1

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Q: Solve the following 3. y* Va - y* dy

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Q: (1 + x)dy – ydx = 0 %3D

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Q: Jo dx 0 1-x² 2 e) fx√x² + 1dx (Hint: use a substitution)

A: Use substitution to solve

Q: dy ycotx + y³cscx dx

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Q: If h(2) = 9 and h'(2) = −5, find d/dx (h(x)/x) x=2

A: If h(2) = 9 and h'(2) = −5, find d/dx (h(x)/x) x=2

Q: If x² + d'y y? = 1, then dx?

A: Given that: x2+y2=1 To find : d2ydx2

Q: if y=6x^5, then dy/dx=

A: We know that; The Power law: ddxxn=nxn-1 And a.f'=a.f' Given: y=6x5