2y (1) (x²+2x) dx = (3 - In x²) dy separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the above dy dx X ==+ + 1 y separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the above y dy + 2x³ + y² = 0 x² dx separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the above (m) (n)

Q: y'(y-1)d(x-y)-(x- y)dy' y2(x- y)² +(1– y')² y'(x- y) arctan tan - 1- y

A: Use the following formulae, to evaluate the given integral.…

Q: x³ y" + xy' - y = 0 [ Hint: x = e¹, ln x = t; x(dy/dx) = dy/dt; x²(d²y/dx²) x³(d³y/dx³) = (d²y/dt2)…

A: The given differential equation, x3y'''+xy'-y=0 We have to find the general solution of the…

Q: 5 find dy/dx for y= [(r^2+1)] ^(-1) ,x= [(4r+1)] ^(1/2) (use chain rule) 5-find for y= (r² + 1)~1 „x…

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Q: Solve Separable (x – 4)y*dx – x³ (y² – 3)dy = 0 -

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Q: 1 (In x+1)x dy dx

A: Given integral is evaluated as follows

Q: dy 3. = (x + y)². dx

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: (x+1)y" -(x +2)y' + y=0;

A: The given equation is (x+1)y''-(x+2)y'+y=0.  We can write this equation as…

Q: How do we find the linearization of g(x, y) = tan−1(xy2) at the point (1, 1). and use linearization…

A: To find the linearization of g(x,y)=tan−1⁡(xy2) at the point (1,1), we willl use the formula for the…

Q: Solve dy (a) dx dy 1+y (b) dx 2x y+1 dy (c) (1+x 2+x dy (d) e*+y

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: y = arccos /1 – x (1-x) 2 1 (1-x) 2 2 JA (1–x) 2 1 (1–x) 2

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Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

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Q: is D.E xy? dx + (x+y) dy= 0 a- linear b- Exact C- non_linear ( Explain that)

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Q: az Find for z = x'y'eV

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Q: dy Find dx in y'sin(x)+y=arctan(x) dy 1-y cos(x)(1+x*) (1+x ]zysin(x)+1 dy 1-y cos(x)(1+x²) dx…

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Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

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Q: Ordinary or Partial Linear or Non- Linear Independent Variable Dependent Variable Order Degree y' =…

A: Given: Differential equation Ordinary or partial Linear or non linear Order Degree Independent…

Q: Let the fame tional J[y] = {² (y² + yy") dx, and the boun dary condition are y (x₂)=0 sy(x₂) = x₁,…

A: Given functional is                          Jy = ∫01y'2+yy''dx  and the boundary conditions are…

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: 4. (sin y - y sin x) dx + (cos x +x cos y- y) dy = 0

A: Note: As per our guidelines we are allowed to solve one question

Q: 1. x(y + 1) dx=(x² + 1)ye dy 2. tan x dx + cot y dy = 0 3. (x + 1) sin y y' + 2x cos y = 0

A: Since you have posted mulipart questions, according to our guidelines we have solved first three…

Q: (i) 2xyy' + y² = 2x² separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in…

A: Answer for (j) : (i) Exact (ii) Homogeneous (iii) Bernoulli in y Answer for (k) : (i) Separable (ii)…

Q: Calculate S (xyz) dz dy dx. (x=1 cy=1-x cz=2-x x=0 Jy=0 Jz=0

A: Solution-

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)