Substitution methods for differential equations: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+2y=12y^2,\ y(0)=\frac{1}{14}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{2x}+ \frac{12}{2}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find v(0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+3y=13y^2,\ y(0)=\frac{1}{15}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{3x}+ \frac{13}{3}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find v(0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+3y=13y^2,\ y(0)=\frac{1}{15}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{3x}+ \frac{13}{3}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find C.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+1y=14y^2,\ y(0)=\frac{1}{16}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{1x}+ \frac{14}{1}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find C.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+1y=14y^2,\ y(0)=\frac{1}{16}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{1x}+ \frac{14}{1}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find y at \(\displaystyle x= \frac{\ln 2}{a}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+2y=15y^2,\ y(0)=\frac{1}{17}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{2x}+ \frac{15}{2}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find y at \(\displaystyle x= \frac{\ln 2}{a}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+2y=15y^2,\ y(0)=\frac{1}{17}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{2x}+ \frac{15}{2}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find y′(0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Substitution methods for differential equations: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle y'+3y=16y^2,\ y(0)=\frac{1}{18}\). Use \(\displaystyle v= \frac{1}{y}\) and write \(\displaystyle v= Ce^{3x}+ \frac{16}{3}\). The specified solution stays nonzero for \(\displaystyle x\ge 0\).
Find y′(0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.