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answerhappygod
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In case an equation is in the form y'= f(az +by+c), ie, the RHS is a linear function of and y. We will use the substitution vaz+by+c to find an implicit general solution. The right hand side of the following first order problem is a linear function of z and y. Use the substitution -y to solve the initial value problem. (5) 5 sin²(z -v). We obtain the following separable equation in the variables and t ✓= Solving this equation and transforming back to the variables a and y we arrive at the implicit solution 14+C Finally we obtain the explict solution of the initial value problem as
In case an equation is in the form y'= f(az +by+c), ie, the RHS is a linear function of and y. We will use the substitution vaz+by+c to find an implicit general solution. The right hand side of the following first order problem is a linear function of z and y. Use the substitution -y to solve the initial value problem. (5) 5 sin²(z -v). We obtain the following separable equation in the variables and t ✓= Solving this equation and transforming back to the variables a and y we arrive at the implicit solution 14+C Finally we obtain the explict solution of the initial value problem as