Combine the Terms Y And $y ^ { \prime }$ Into the Derivative of a Product, Then Solve the Equation

question 56

True/False

Combine the terms y and $y ^ { \prime }$ into the derivative of a product, then solve the equation. $\mathrm { e } ^ { 3 \mathrm { t } ^ { 2 } } \mathrm { y } ^ { \prime } + 6 \mathrm { te } ^ { 3 \mathrm { t } ^ { 2 } } \mathrm { y } = \frac { 5 \sqrt { \mathrm { t } } } { 4 }$ . Is this the solution: $y = \frac { 5 } { 6 } t ^ { 3 / 2 } e ^ { - 3 t ^ { 2 } } + C e ^ { - 3 t ^ { 2 } } ?$

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Definitions:

Sexual Reproduction

The process by which organisms produce offspring through the combination of genetic materials from two different cells, typically involving male and female gametes.

Genetic Diversity

The total number of genetic characteristics in the genetic makeup of a species, contributing to its ability to adapt and survive changes.

Asexual Reproduction

A mode of reproduction that does not involve the fusion of gametes, resulting in offspring genetically identical to the parent.

Diploid Cells

Cells that have two complete sets of chromosomes, one from each parent, characteristic of most organisms’ body cells.