Question 1: Question 2: Consider the equation (5xy + 6xy + 4xy) dx + (2x +...

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Question 1: Question 2: Consider the equation (5x²y + 6x³y² + 4xy²) dx + (2x³ + 3x+y + 3x²y) dy = 0. (a) Show that the equation is not exact. (b) Multiply the equation by x"y" and determine values for n and m that make the resulting equa- tion exact. (c) Use the solution of the resulting exact equation to solve the original equation. (18) Riccati Equation. An equation of the form dy dx = P(x)y² + Q(x)y + R(x) is called a generalized Riccati equation.* (a) If one solution-say, u(x)-of (18) is known, show that the substitution y = u + 1/v reduces (18) to a linear equation in v. (b) Given that u(x) = x is a solution to dy ² = x²³ ( y − x)² + ²/2 ₁ - dx use the result of part (a) to find all the other solu- tions to this equation. (The particular solution Question 1: Question 2: Consider the equation (5x²y + 6x³y² + 4xy²) dx + (2x³ + 3x+y + 3x²y) dy = 0. (a) Show that the equation is not exact. (b) Multiply the equation by x"y" and determine values for n and m that make the resulting equa- tion exact. (c) Use the solution of the resulting exact equation to solve the original equation. (18) Riccati Equation. An equation of the form dy dx = P(x)y² + Q(x)y + R(x) is called a generalized Riccati equation.* (a) If one solution-say, u(x)-of (18) is known, show that the substitution y = u + 1/v reduces (18) to a linear equation in v. (b) Given that u(x) = x is a solution to dy ² = x²³ ( y − x)² + ²/2 ₁ - dx use the result of part (a) to find all the other solu- tions to this equation. (The particular solution